SOLUTION: Factor each expression completely. 1. 12x2 + 6x + 18 3(2x2 + x + 3) 6(2x2 + x + 3) 3(2x � 1)(x + 3) 6(2x � 1)(x + 3) 2. m2 + 11m + 18 (m � 2)(m + 9) (m

Question 171535:

Factor each expression completely.
1. 12x2 + 6x + 18
3(2x2 + x + 3)
6(2x2 + x + 3)
3(2x � 1)(x + 3)
6(2x � 1)(x + 3)
2. m2 + 11m + 18
(m � 2)(m + 9)
(m + 2)(m + 9)
(m � 3)(m + 6)
(m + 3)(m + 6)
3. x2 � 14x � 15
(x � 5)(x + 3)
(x + 5)(x � 3)
(x � 15)(x + 1)
(x + 15)(x � 1)
4. x2 � 13x + 42
(x + 6)(x � 7)
(x � 6)(x + 7)
(x � 6)(x � 7)
(x + 6)(x + 7)
5. 64x2 + 144x + 81
(8x � 9)2
(8x + 9)2
2(8x + 9)
(8x + 9)(8x � 9)
6. 3x2 + 5x � 50
(x � 25)(3x + 2)
(3x � 25)(x + 2)
(x � 10)(3x + 5)
(3x � 10)(x + 5)
7. 5k2 � 125
(k � 5)2
5(k � 5)2
(k + 5)(k � 5)
5(k + 5)(k � 5)
8. 15n2 � 8n +1
(5n + 1)(3n + 1)
(5n � 1)(3n � 1)
(5n + 1)(3n � 1)
(5n � 1)(3n + 1)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first three to get you started

# 1

Start with the given expression

Factor out the GCF

Now let's focus on the inner expression

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Looking at we can see that the first term is and the last term is where the coefficients are 2 and 3 respectively.

Now multiply the first coefficient 2 and the last coefficient 3 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient 1? Let's list all of the factors of 6:

Factors of 6:
1,2,3,6

-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 6
1*6
2*3
(-1)*(-6)
(-2)*(-3)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1

First Number	Second Number	Sum
1	6	1+6=7
2	3	2+3=5
-1	-6	-1+(-6)=-7
-2	-3	-2+(-3)=-5

None of these pairs of factors add to 1. So the expression cannot be factored

So just remains as

------------------------------------------------------------

Answer:

So factors to

# 2

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 18 respectively.

Now multiply the first coefficient 1 and the last coefficient 18 to get 18. Now what two numbers multiply to 18 and add to the middle coefficient 11? Let's list all of the factors of 18:

Factors of 18:
1,2,3,6,9,18

-1,-2,-3,-6,-9,-18 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 18
1*18
2*9
3*6
(-1)*(-18)
(-2)*(-9)
(-3)*(-6)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 11

First Number	Second Number	Sum
1	18	1+18=19
2	9	2+9=11
3	6	3+6=9
-1	-18	-1+(-18)=-19
-2	-9	-2+(-9)=-11
-3	-6	-3+(-6)=-9

From this list we can see that 2 and 9 add up to 11 and multiply to 18

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

------------------------------------------------------------

Answer:
So factors to

# 3

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -15 respectively.

Now multiply the first coefficient 1 and the last coefficient -15 to get -15. Now what two numbers multiply to -15 and add to the middle coefficient -14? Let's list all of the factors of -15:

Factors of -15:
1,3,5,15

-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -15
(1)*(-15)
(3)*(-5)
(-1)*(15)
(-3)*(5)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -14

First Number	Second Number	Sum
1	-15	1+(-15)=-14
3	-5	3+(-5)=-2
-1	15	-1+15=14
-3	5	-3+5=2

From this list we can see that 1 and -15 add up to -14 and multiply to -15

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

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